Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligations will resemble a perpetuity. Suppose that you are managing a pension fund with obligations to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%.
a) If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupons of 6% (paid annually) is 11 years, how much investment in these two bonds will be necessary to both fully fund and immunize your obligation.
b) If the face value of both bonds is $1,000, how many 20-year bonds would need to be purchases in a)?